[Serve] Optimize the _get_live_deployments function

[jugalshah291]

Description

The _get_live_deployments function internally iterates over self._deployment_state ( that stores all the live deployments) and filters out deployment for a specific app. This is inefficient especially when you have a large of serve application running. (For every serve application we are iterating over all the deployments)

May be we can optimize it by defining a new dictionary (in place of self._deployment_state) that maps app name to the live deployments name. However I don't know much about the ray internals and their could be a better way around this

Use case

Our system is running a very large number of DeploymentHandles (see #44784 for more details). We've noticed that the Serve controller gets overloaded (>100% CPU usage) and a small percentage of this CPU usage is coming from the _get_live_deployments function, which is called at multiple places.

[jugalshah291]

Accidentally created a duplicate issue